We model the surface brightness profiles of an observed sample of 119 Abell Brightest Cluster Galaxies (BCG), finding a generalised deVaucouleurs r^1/n law, where n is a free parameter, to be appropriate. BCG typically have values of n greater than 4. The shape parameter n is shown to correlate with effective half-light radius, r_e, such that the larger BCG have larger values of n. This continues a trend noticed amongst ordinary elliptical galaxies and dwarf ellipticals, such that the brighter galaxies have larger values of n. Departures from the r^1/4 law are found to be a real feature of galaxy profiles, not due to observational errors or coupling of n with the other model parameters.